#include "f2c.h"
#include "blaswrap.h"

/* Table of constant values */

static doublereal c_b8 = -1.;
static integer c__1 = 1;

/* Subroutine */ int dpbtf2_(char *uplo, integer *n, integer *kd, doublereal *
	ab, integer *ldab, integer *info)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, i__1, i__2, i__3;
    doublereal d__1;

    /* Builtin functions */
    double sqrt(doublereal);

    /* Local variables */
    integer j, kn;
    doublereal ajj;
    integer kld;
    extern /* Subroutine */ int dsyr_(char *, integer *, doublereal *, 
	    doublereal *, integer *, doublereal *, integer *), dscal_(
	    integer *, doublereal *, doublereal *, integer *);
    extern logical lsame_(char *, char *);
    logical upper;
    extern /* Subroutine */ int xerbla_(char *, integer *);


/*  -- LAPACK routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  DPBTF2 computes the Cholesky factorization of a real symmetric */
/*  positive definite band matrix A. */

/*  The factorization has the form */
/*     A = U' * U ,  if UPLO = 'U', or */
/*     A = L  * L',  if UPLO = 'L', */
/*  where U is an upper triangular matrix, U' is the transpose of U, and */
/*  L is lower triangular. */

/*  This is the unblocked version of the algorithm, calling Level 2 BLAS. */

/*  Arguments */
/*  ========= */

/*  UPLO    (input) CHARACTER*1 */
/*          Specifies whether the upper or lower triangular part of the */
/*          symmetric matrix A is stored: */
/*          = 'U':  Upper triangular */
/*          = 'L':  Lower triangular */

/*  N       (input) INTEGER */
/*          The order of the matrix A.  N >= 0. */

/*  KD      (input) INTEGER */
/*          The number of super-diagonals of the matrix A if UPLO = 'U', */
/*          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0. */

/*  AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,N) */
/*          On entry, the upper or lower triangle of the symmetric band */
/*          matrix A, stored in the first KD+1 rows of the array.  The */
/*          j-th column of A is stored in the j-th column of the array AB */
/*          as follows: */
/*          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; */
/*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd). */

/*          On exit, if INFO = 0, the triangular factor U or L from the */
/*          Cholesky factorization A = U'*U or A = L*L' of the band */
/*          matrix A, in the same storage format as A. */

/*  LDAB    (input) INTEGER */
/*          The leading dimension of the array AB.  LDAB >= KD+1. */

/*  INFO    (output) INTEGER */
/*          = 0: successful exit */
/*          < 0: if INFO = -k, the k-th argument had an illegal value */
/*          > 0: if INFO = k, the leading minor of order k is not */
/*               positive definite, and the factorization could not be */
/*               completed. */

/*  Further Details */
/*  =============== */

/*  The band storage scheme is illustrated by the following example, when */
/*  N = 6, KD = 2, and UPLO = 'U': */

/*  On entry:                       On exit: */

/*      *    *   a13  a24  a35  a46      *    *   u13  u24  u35  u46 */
/*      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56 */
/*     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66 */

/*  Similarly, if UPLO = 'L' the format of A is as follows: */

/*  On entry:                       On exit: */

/*     a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66 */
/*     a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   * */
/*     a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    * */

/*  Array elements marked * are not used by the routine. */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters. */

    /* Parameter adjustments */
    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1;
    ab -= ab_offset;

    /* Function Body */
    *info = 0;
    upper = lsame_(uplo, "U");
    if (! upper && ! lsame_(uplo, "L")) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*kd < 0) {
	*info = -3;
    } else if (*ldab < *kd + 1) {
	*info = -5;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DPBTF2", &i__1);
	return 0;
    }

/*     Quick return if possible */

    if (*n == 0) {
	return 0;
    }

/* Computing MAX */
    i__1 = 1, i__2 = *ldab - 1;
    kld = max(i__1,i__2);

    if (upper) {

/*        Compute the Cholesky factorization A = U'*U. */

	i__1 = *n;
	for (j = 1; j <= i__1; ++j) {

/*           Compute U(J,J) and test for non-positive-definiteness. */

	    ajj = ab[*kd + 1 + j * ab_dim1];
	    if (ajj <= 0.) {
		goto L30;
	    }
	    ajj = sqrt(ajj);
	    ab[*kd + 1 + j * ab_dim1] = ajj;

/*           Compute elements J+1:J+KN of row J and update the */
/*           trailing submatrix within the band. */

/* Computing MIN */
	    i__2 = *kd, i__3 = *n - j;
	    kn = min(i__2,i__3);
	    if (kn > 0) {
		d__1 = 1. / ajj;
		dscal_(&kn, &d__1, &ab[*kd + (j + 1) * ab_dim1], &kld);
		dsyr_("Upper", &kn, &c_b8, &ab[*kd + (j + 1) * ab_dim1], &kld, 
			 &ab[*kd + 1 + (j + 1) * ab_dim1], &kld);
	    }
/* L10: */
	}
    } else {

/*        Compute the Cholesky factorization A = L*L'. */

	i__1 = *n;
	for (j = 1; j <= i__1; ++j) {

/*           Compute L(J,J) and test for non-positive-definiteness. */

	    ajj = ab[j * ab_dim1 + 1];
	    if (ajj <= 0.) {
		goto L30;
	    }
	    ajj = sqrt(ajj);
	    ab[j * ab_dim1 + 1] = ajj;

/*           Compute elements J+1:J+KN of column J and update the */
/*           trailing submatrix within the band. */

/* Computing MIN */
	    i__2 = *kd, i__3 = *n - j;
	    kn = min(i__2,i__3);
	    if (kn > 0) {
		d__1 = 1. / ajj;
		dscal_(&kn, &d__1, &ab[j * ab_dim1 + 2], &c__1);
		dsyr_("Lower", &kn, &c_b8, &ab[j * ab_dim1 + 2], &c__1, &ab[(
			j + 1) * ab_dim1 + 1], &kld);
	    }
/* L20: */
	}
    }
    return 0;

L30:
    *info = j;
    return 0;

/*     End of DPBTF2 */

} /* dpbtf2_ */
